{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#In-this-notebook,\" data-toc-modified-id=\"In-this-notebook,-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>In this notebook,</a></span></li><li><span><a href=\"#Expected-utility-via-Monte-Carlo\" data-toc-modified-id=\"Expected-utility-via-Monte-Carlo-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Expected utility via Monte Carlo</a></span><ul class=\"toc-item\"><li><span><a href=\"#Plotting-the-exact-solution\" data-toc-modified-id=\"Plotting-the-exact-solution-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Plotting the exact solution</a></span></li><li><span><a href=\"#MC-implementation\" data-toc-modified-id=\"MC-implementation-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>MC implementation</a></span></li></ul></li><li><span><a href=\"#Exercise\" data-toc-modified-id=\"Exercise-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Exercise</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# 4. Expected utility and Monte Carlo in Python\n",
    "**Camilo A. Garcia Trillos - 2020**\n",
    "\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "## In this notebook,\n",
    "- we look at the Monte Carlo method and how to use it to approximate expected utilities or certainty equivalents.\n",
    "- we use Python to plot information using matplotlib, including a histogram and a regression\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us import some packages: math, numpy, matplotlib and scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from numpy.random import default_rng  #  pseudo-random number generator\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# This is an indicator to tell jupyter notebook to show us all plots inline:\n",
    "%matplotlib inline \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Expected utility via Monte Carlo\n",
    "\n",
    "To compute the expected utility of a wealth gamble $W$ we can use he law of large numbers. Indeed, if $E[|u(W)|]<\\infty$, we have\n",
    "$$  \\frac{1}{N} \\sum_{i=1}^N u(W_i)  \\rightarrow \\mathbb E[u(W)] \\text{ as } N\\rightarrow \\infty,$$\n",
    "where $(W_i)$ is a family of independent draws of random variables with $W_i \\sim W$ for each $i$.\n",
    "\n",
    "The Monte Carlo method relies on this equality to produce an approximation to the expectation (by choosing a large N and calculating the empirical average).\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
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   "source": [
    "To see how this works, let us start with $W$ being normally distributed, that is $W = \\sigma N + \\mu$, where $\\mu, \\sigma \\in \\mathbb R$ and $N$ is standard normally distributed.  \n",
    "\n",
    "Now, let us suppose first we want to compute expected utility of a CARA utility $u(x) = 1-\\exp(-\\alpha * x)$. We can calculate explicitly\n",
    "$$ \\mathbb E[u(W)] = \\mathbb E[1- \\exp(-\\alpha \\sigma N - \\alpha \\mu  ))] =1- \\exp\\left(-\\alpha \\mu + \\frac 1 2 \\alpha^2 \\sigma^2  \\right).$$\n",
    "\n",
    "We use this value to compare to the value approximated by Monte Carlo as explained before. Let us build a plot of this function in some given domain."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### Plotting the exact solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "There are several libraries allowing us to plot in Python. We will use one of the simplest: Matplotlib.\n",
    "\n",
    "A simple way to plot in this library is to provide it with vectors of input and output. To try it, let us simply plot the result of the (exact) expected utility when the CARA coefficient changes.\n",
    "\n",
    "We start by sampling the space of coefficients of risk aversion:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.00000000e-03 3.12929293e-02 6.15858586e-02 9.18787879e-02\n",
      " 1.22171717e-01 1.52464646e-01 1.82757576e-01 2.13050505e-01\n",
      " 2.43343434e-01 2.73636364e-01 3.03929293e-01 3.34222222e-01\n",
      " 3.64515152e-01 3.94808081e-01 4.25101010e-01 4.55393939e-01\n",
      " 4.85686869e-01 5.15979798e-01 5.46272727e-01 5.76565657e-01\n",
      " 6.06858586e-01 6.37151515e-01 6.67444444e-01 6.97737374e-01\n",
      " 7.28030303e-01 7.58323232e-01 7.88616162e-01 8.18909091e-01\n",
      " 8.49202020e-01 8.79494949e-01 9.09787879e-01 9.40080808e-01\n",
      " 9.70373737e-01 1.00066667e+00 1.03095960e+00 1.06125253e+00\n",
      " 1.09154545e+00 1.12183838e+00 1.15213131e+00 1.18242424e+00\n",
      " 1.21271717e+00 1.24301010e+00 1.27330303e+00 1.30359596e+00\n",
      " 1.33388889e+00 1.36418182e+00 1.39447475e+00 1.42476768e+00\n",
      " 1.45506061e+00 1.48535354e+00 1.51564646e+00 1.54593939e+00\n",
      " 1.57623232e+00 1.60652525e+00 1.63681818e+00 1.66711111e+00\n",
      " 1.69740404e+00 1.72769697e+00 1.75798990e+00 1.78828283e+00\n",
      " 1.81857576e+00 1.84886869e+00 1.87916162e+00 1.90945455e+00\n",
      " 1.93974747e+00 1.97004040e+00 2.00033333e+00 2.03062626e+00\n",
      " 2.06091919e+00 2.09121212e+00 2.12150505e+00 2.15179798e+00\n",
      " 2.18209091e+00 2.21238384e+00 2.24267677e+00 2.27296970e+00\n",
      " 2.30326263e+00 2.33355556e+00 2.36384848e+00 2.39414141e+00\n",
      " 2.42443434e+00 2.45472727e+00 2.48502020e+00 2.51531313e+00\n",
      " 2.54560606e+00 2.57589899e+00 2.60619192e+00 2.63648485e+00\n",
      " 2.66677778e+00 2.69707071e+00 2.72736364e+00 2.75765657e+00\n",
      " 2.78794949e+00 2.81824242e+00 2.84853535e+00 2.87882828e+00\n",
      " 2.90912121e+00 2.93941414e+00 2.96970707e+00 3.00000000e+00]\n"
     ]
    }
   ],
   "source": [
    "x = np.linspace(0.001,3,100) # creates a vector of size 100 with numbers between 0.1 and 30\n",
    "print(x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We now implement the exact solution expected CARA utility under normal assumptions. Since it is a simple expression, we can use a lambda function as introduced before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# The operations in expected_u are well defined for vectors as long as mu,sd,x broadcast correctly together.\n",
    "expected_u = lambda mu,sigma,alpha: 1-np.exp(-alpha*mu+0.5*alpha**2*sigma**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Note that we use 'np.exp' and not 'math.exp': this is because we want the function to be 'vectorial', that is, to accept vectors as an input \n",
    "\n",
    "(try changing np.exp for math.exp, run the code and then run the code below... there will be an error)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 4.98553078e-03  1.43161779e-01  2.59436323e-01  3.57578415e-01\n",
      "  4.40665016e-01  5.11214871e-01  5.71295417e-01  6.22608244e-01\n",
      "  6.66557592e-01  7.04305396e-01  7.36815622e-01  7.64890079e-01\n",
      "  7.89197408e-01  8.10296616e-01  8.28656217e-01  8.44669848e-01\n",
      "  8.58669036e-01  8.70933653e-01  8.81700514e-01  8.91170449e-01\n",
      "  8.99514138e-01  9.06876943e-01  9.13382902e-01  9.19138057e-01\n",
      "  9.24233215e-01  9.28746256e-01  9.32744058e-01  9.36284107e-01\n",
      "  9.39415849e-01  9.42181820e-01  9.44618597e-01  9.46757599e-01\n",
      "  9.48625755e-01  9.50246068e-01  9.51638082e-01  9.52818282e-01\n",
      "  9.53800408e-01  9.54595733e-01  9.55213272e-01  9.55659954e-01\n",
      "  9.55940751e-01  9.56058773e-01  9.56015322e-01  9.55809920e-01\n",
      "  9.55440295e-01  9.54902345e-01  9.54190056e-01  9.53295395e-01\n",
      "  9.52208157e-01  9.50915768e-01  9.49403046e-01  9.47651906e-01\n",
      "  9.45640992e-01  9.43345252e-01  9.40735416e-01  9.37777378e-01\n",
      "  9.34431459e-01  9.30651531e-01  9.26383973e-01  9.21566425e-01\n",
      "  9.16126303e-01  9.09979026e-01  9.03025898e-01  8.95151561e-01\n",
      "  8.86220947e-01  8.76075607e-01  8.64529284e-01  8.51362567e-01\n",
      "  8.36316424e-01  8.19084342e-01  7.99302784e-01  7.76539543e-01\n",
      "  7.50279522e-01  7.19907310e-01  6.84685798e-01  6.43729854e-01\n",
      "  5.95973852e-01  5.40131507e-01  4.74646078e-01  3.97628461e-01\n",
      "  3.06780053e-01  1.99296367e-01  7.17463012e-02 -8.00794903e-02\n",
      " -2.61359526e-01 -4.78482558e-01 -7.39352719e-01 -1.05377686e+00\n",
      " -1.43395752e+00 -1.89512203e+00 -2.45632757e+00 -3.14149420e+00\n",
      " -3.98073414e+00 -5.01206692e+00 -6.28363866e+00 -7.85660183e+00\n",
      " -9.80886243e+00 -1.22399700e+01 -1.52775168e+01 -1.90855369e+01]\n"
     ]
    }
   ],
   "source": [
    "sd, mu = 2,5  # Equivalently sd=2 and mu=5\n",
    "y=expected_u(mu,sd,x) # Note that x is a vector\n",
    "print(y) # And so is y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "If for some reason you cannot implement directly a vectorial function, it is possible to use a loop or the function np.vectorize to render the function vector ready."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We are ready to make the plot:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Expected utility')"
      ]
     },
     "execution_count": 26,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 26,
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 521
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.plot(x,y,'b--')   # Make a plot between x and y\n",
    "plt.title('Expected utility as a function of coefficient of absolute risk aversion - Gaussian case') # Add a title\n",
    "plt.xlabel('Coefficient of risk aversion') # Add a label on the x axis\n",
    "plt.ylabel('Expected utility') # Add a label on the y axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "### MC implementation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Let us now look at the Monte Carlo approximation of the above function. We start by defining a function that calculates the CARA utility:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
   ],
   "source": [
    "cara_utility = lambda x,alpha: 1-np.exp(-alpha*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "# Some tests on our function\n",
    "assert cara_utility(1,1)== 1-1./math.e , \"Failed test with x=1, alpha =1\"\n",
    "assert cara_utility(5,2)== 1-math.e**-10., \"Failed test with x=5, alpha=2\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can now generate a sample of wealths, distributed like a $\\mathcal N (\\mu,\\sigma^2)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "sd, mu = 2,5  # Equivalently sd=2 and mu=5\n",
    "N = 10000\n",
    "rng = default_rng()\n",
    "sample_gaussian = rng.normal(mu,sd,N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "How can we check that these are Gaussian? We can plot the histogram of the empirical distribution defined. The package matplotlib has a convenient function for this: *plt.hist* (recall that plt is our alias for pyplot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'density')"
      ]
     },
     "execution_count": 18,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 18,
     "metadata": {
      "image/png": {
       "height": 277,
       "width": 398
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.hist(sample_gaussian, density=True)  # Plots the histogram, normalising to obtain a pdf.\n",
    "plt.title('Histogram of our sample') # Add a title to the plot\n",
    "plt.xlabel('sample_gaussian') # Add a label on the X axis\n",
    "plt.ylabel('density') # Add a label on the Y axis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "It looks like a good Gaussian sample with our parameters (centred in 5 and with standard deviation 2). In later notebooks we will learn some alternative ways for checking Gaussianity. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We can now calculate a Monte Carlo approximation of our expected utility. Examine the code below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9505191425518782"
      ]
     },
     "execution_count": 19,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cara_utility(sample_gaussian,1).mean()  # In one line, we evaluate the cara utility for each entry of the sample, and then calculate the mean of the resulting vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Observe now the following: the estimation is random. To see this, let us run the estimation with another sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9512317213956805"
      ]
     },
     "execution_count": 20,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cara_utility(rng.normal(mu,sd,N),1).mean()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "As expected, the two values are close but different. Indeed, this estimator is **random**, because it depends on the sample, which is itself random. This is something to be taken into account when using Monte Carlo estimators. \n",
    "\n",
    "In fairness, the Python implementation of the MC estimator can only produce a pseudo-random generation. To see this, we can fix the seed of the pseudo-random generation algorithm and compare the answers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0\n"
     ]
    }
   ],
   "source": [
    "rng = default_rng(1234)\n",
    "sample_gaussian = rng.normal(mu,sd,N)\n",
    "mc_eu1 = cara_utility(sample_gaussian,1).mean()\n",
    "rng = default_rng(1234)\n",
    "sample_gaussian2 = rng.normal(mu,sd,N)\n",
    "mc_eu2 = cara_utility(sample_gaussian2,1).mean()\n",
    "print(mc_eu1-mc_eu2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Setting the random states allows us to repeat the same sequence on the pseudo-random generation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "Now, let us remind ourselves of the closed form solution:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.950212931632136"
      ]
     },
     "execution_count": 22,
     "metadata": {
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "expected_u(mu,sd,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "We see that the value is very close to the value(s) estimated via MC. Indeed, this error can be explained via the central limit theorem, which give us a control on the L_2 norm and is of the form\n",
    "\n",
    "$$\\left \\|\\mathbb E[u(W)] - \\frac 1 N \\sum_{i=1}^N u(W_i)    \\right \\|_{L_2} \\leq \\frac{C}{N^{1/2}} {\\rm sd}(X_1)  $$\n",
    "\n",
    "Let us verify this empirically, using a plot and a regression. We want to retrieve the rate of convergence, which is the power 1/2 in the above control. To do this we use a log-log plot (think why)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7faa48cb9e80>"
      ]
     },
     "execution_count": 23,
     "metadata": {
     },
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "execution_count": 23,
     "metadata": {
      "image/png": {
       "height": 278,
       "width": 517
      },
      "needs_background": "light"
     },
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_vec = 2**np.arange(10,20) # The number of MC simulations, we take powers of 2\n",
    "rng = default_rng(1) # Fix the seed to \"1\", so that the plot looks the same every time you run it\n",
    "u = np.array([cara_utility(rng.normal(mu,sd,N),1).mean() for N in n_vec])  # Create an MC expected utility for the sizes above\n",
    "error = np.abs(u - expected_u(mu, sd, 1)) # Calculate the error\n",
    "plt.loglog(n_vec, error, 'ro', label='Error') # Make a log log plot\n",
    "plt.title('Error in Monte Carlo Expected utility as a function of size of sample - Gaussian case')\n",
    "plt.xlabel('N')\n",
    "plt.ylabel('Error')\n",
    "\n",
    "# Let us also add a reference line. To do so, we need to calculate a simple regression. We can use the polyfit function\n",
    "m, b = np.polyfit( np.log(n_vec), np.log(error), 1)\n",
    "plt.loglog(n_vec, np.exp(b+m*np.log(n_vec)), 'g--', label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "The hardest line of code in the plot above is possibly\n",
    "```python\n",
    "plt.loglog(n_vec, np.exp(b+m*np.log(n_vec)), 'g--', label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "```\n",
    "\n",
    "Let us look at two parts in particular:\n",
    "\n",
    "```python\n",
    "'g--'\n",
    "```\n",
    "Means make a green dashed line.\n",
    "\n",
    "while \n",
    "```python\n",
    "label='Best fit: Error ='+ \"%.2f N^(%.2f)\" % (math.exp(b),m))   \n",
    "```\n",
    "means: take the value of exp(b), round it to a float with two decimal figures, do the same with m, and write a string that contains exp(b) N^ m with this format. This is saved on a variable label that is used by matplotlib to assign the legends in a plot.\n",
    "\n",
    "Check that you understand the other lines of code."
   ]
  },
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   "source": [
    "Note that the best fit slope is close to -1/2 as expected. This is consistent with the theoretical error given before. **Write the equations to be sure you understand why.**"
   ]
  },
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   "source": [
    "## Exercise\n",
    "\n",
    "1. Compute, via a Monte-Carlo simulation, the expected utility of a CRRA investor for the following gambles.\n",
    "    - $W_1 \\sim |aN + b|$, where $N$ is standard normally distributed and $a,b \\in R$.\n",
    "    - $W_2 \\sim \\text{Exp}(\\lambda_2)$ where $\\lambda_2>0$.\n",
    "\t\n",
    "You might have to look up online the commands for the corresponding random number generators. (Use the ones in numpy.random)."
   ]
  },
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   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
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   ],
   "source": [
    "import numpy as np\n",
    "def MC_expected_u1(a,b,n,rho):\n",
    "    if rho == 1:\n",
    "        crra_u = lambda x:np.log(x)\n",
    "    else:\n",
    "        crra_u = lambda x,rho:(x**(1-rho))/(1-rho)\n",
    "    rng = np.random.default_rng()\n",
    "    return (crra_u((np.abs(rng.normal(b,a,n))),rho)).mean()\n",
    "\n",
    "def MC_expected_u2(lamda,n,rho):\n",
    "    if rho == 1:\n",
    "        crra_u = lambda x:np.log(x)\n",
    "    else:\n",
    "        crra_u = lambda x,rho:(x**(1-rho))/(1-rho)\n",
    "    rng = np.random.default_rng()\n",
    "    return (crra_u(rng.exponential(1/lamda,n), rho)).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "2. Write a function that computes the certainty equivalent for a CRRA investor. (Hint: You might have to compute, on a piece of paper, $u^{-1}$ for the different relative risk aversions $\\rho$.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
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   "outputs": [
   ],
   "source": [
    "def certainty_equivalent1(a,b,n,rho):\n",
    "    if rho == 1:\n",
    "        u_inverse = lambda x:np.exp(x)\n",
    "        return u_inverse(MC_expected_u1(a, b, n, rho))\n",
    "    else:\n",
    "        u_inverse = lambda x,y:((1-y)*x)**(1/(1-y))\n",
    "        return u_inverse(MC_expected_u1(a, b, n, rho),rho)\n",
    "\n",
    "\n",
    "def certainty_equivalent2(lamda,n,rho):\n",
    "    if rho == 1:\n",
    "        u_inverse = lambda x:np.exp(x)\n",
    "        return u_inverse(MC_expected_u2(lamda, n, rho))\n",
    "    else:\n",
    "        u_inverse = lambda x,y:((1-y)*x)**(1/(1-y))\n",
    "        return u_inverse(MC_expected_u2(lamda,n,rho),rho)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": false
   },
   "source": [
    "3. With $a = 1$ and $b = 2$, plot the certainty equivalent of a CRRA investor as a function of relative risk aversion $\\rho$, using gamble $W_1$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
   ],
   "source": [
    "x = np.linspace(-1,3,1000)\n",
    "y = np.array([certainty_equivalent1(1,2,10000,rho) for rho in x])\n",
    "plt.plot(x,y)\n",
    "plt.show()\n"
   ]
  }
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